Sampling requirements in near-field ptychography

Ptychography is a robust lensless form of microscopy routinely used for applications spanning life and physical sciences. The most common ptychography setup consists in using a detector to record diffraction patterns in the far-field. A near-field version has been more recently introduced, and its potential is yet to be fully exploited. In this work, the sampling requirements for near-field ptychography are analysed. Starting from the characterisation available in literature, the formalism of the fractional Fourier transform is used to generalise analytically the sampling conditions. The results harmonise the far- and near-field regimes and widen the applications of the technique with respect to the current knowledge. This study is supported by simulations and provides clear guidelines on how to optimise the setup and acquisition strategies for near-field ptychography experiments. The results are key to drive the translation of the technique towards low brilliance sources.